Local hypergraph clustering using capacity releasing diffusion.

Area of Science:

• Machine Learning
• Graph Theory
• Data Mining

Background:

• Local graph clustering aims to identify dense subgraphs around seed nodes.
• Higher-order information significantly improves graph clustering performance.
• Existing methods often rely on spectral graph theory, but max-flow/min-cut approaches offer alternative guarantees.

Purpose of the Study:

• To propose a novel local hypergraph clustering technique, hypergraph capacity releasing diffusion (HG-CRD).
• To extend the capacity releasing diffusion (CRD) method to leverage higher-order patterns represented by hyperedges.
• To theoretically analyze HG-CRD's performance using motif conductance.

Main Methods:

• Extension of the capacity releasing diffusion (CRD) algorithm to hypergraphs.
• Development of the hypergraph CRD (HG-CRD) method for local hypergraph clustering.
• Theoretical analysis of HG-CRD using motif conductance.

Main Results:

• HG-CRD effectively clusters data based on higher-order patterns in hypergraphs.
• The method provides theoretical guarantees related to motif conductance.
• Experimental results demonstrate enhanced clustering quality on synthetic and real-world datasets compared to existing techniques.

Conclusions:

• HG-CRD represents a significant advancement in local graph clustering by incorporating hypergraph structures.
• The proposed method offers improved performance and theoretical underpinnings for clustering based on higher-order relationships.
• HG-CRD shows promise for applications requiring the analysis of complex, multi-way relationships in data.